Let's first find out how many children Mrs. Gomez has in total. We know that she has 2 boys. The problem states that the number of children she has is three times the number of boys. Therefore, we can set up the following equation:
Let \( B \) = number of boys = 2
Let \( C \) = number of children
From the problem, we have:
\[ C = 3B \]
Substituting the value for \( B \):
\[ C = 3 \times 2 = 6 \]
Therefore, Mrs. Gomez has a total of 6 children. Since she has 2 boys, she must have:
\[ G = C - B = 6 - 2 = 4 \]
So she has 4 girls.
Now we have:
- Number of girls (G) = 4
- Number of boys (B) = 2
Next, we calculate the ratio of girls to boys:
\[ \text{Ratio of girls to boys} = \frac{G}{B} = \frac{4}{2} = 2:1 \]
Now we can see which bouquet matches the 2:1 ratio of pink flowers to blue flowers.
Let's evaluate the provided bouquet options:
-
Bouquet of 12 flowers: 4 pink and 8 blue
- Ratio = \( \frac{4}{8} = \frac{1}{2} \) (Not 2:1)
-
Bouquet of 14 flowers: 8 pink and 6 blue
- Ratio = \( \frac{8}{6} = \frac{4}{3} \) (Not 2:1)
-
Bouquet of 15 flowers: 6 pink and 9 blue
- Ratio = \( \frac{6}{9} = \frac{2}{3} \) (Not 2:1)
-
Bouquet of 18 flowers: 12 pink and 6 blue
- Ratio = \( \frac{12}{6} = 2 \) (This equals 2:1)
The largest bouquet that matches the girl's to boy's ratio of 2:1 is:
The bouquet of 18 flowers, 12 pink and 6 blue.